Linear variable differential transformers for high precision position measurements

ABSTRACT

A linear variable transformer (LVDT) for use in a transducer. The LVDT has a non-ferromagnetic core which may eliminate Barkhausen noise and thereby improve the sensitivity of the resulting measurements. In one aspect, this system may be used in an atomic force microscope.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/683,592, filed Oct. 10, 2003, which is a divisional of U.S. patentapplication Ser. No. 10/016,475, filed Nov. 30, 2001, which claims thebenefit of U.S. provisional application No. 60/250,313, filed Nov. 30,2000, and U.S. provisional application No. 60/332,243, filed on Nov. 16,2001. The disclosures of the prior applications are considered part of(and are incorporated by reference in) the disclosure of thisapplication.

REFERENCES CITED

U.S. Patent Documents

-   U.S. Pat. No. 2,364,237 December 1944 Neff 340/199-   U.S. Pat. No. 2,452,862 November 1948 Neff 340/xxx-   U.S. Pat. No. 2,503,851 April 1950 Snow 340/196-   U.S. Pat. No. 4,030,085 June 1977 Ellis et al. 340/199-   U.S. Pat. No. 4,634,126 January 1987 Kimura 273/129-   U.S. Pat. No. 4,669,300 June 1987 Hall et al. 73/105-   U.S. Pat. No. 4,705,971 November 1987 Nagasaka 310/12-   U.S. Pat. No. 5,414,939 May 1995 Waugaman 33/522-   U.S. Pat. No. 5,461,319 October 1995 Peters 324/660-   U.S. Pat. No. 5,465,046 November 1995 Campbell et al. 324/244-   U.S. Pat. No. 5,469,053 November 1995 Laughlin 324/207.18-   U.S. Pat. No. 5,477,473 December 1995 Mandl et al. 364/576-   U.S. Pat. No. 5,513,518 May 1996 Lindsay 73/105-   U.S. Pat. No. 5,705,741 January 1998 Eaton et al. 73/105-   U.S. Pat. No. 5,739,686 May 1998 Naughton et al. 324/259-   U.S. Pat. No. 5,767,670 June 1998 Mahler et al. 324/207.12-   U.S. Pat. No. 5,777,468 July 1998 Mahler 324/207.18-   U.S. Pat. No. 5,948,972 September 1999 Samsavar et al. 73/105-   U.S. Pat. No. 6,267,005 July 2001 Samsavar et al. 73/105    Other Publications-   Bertram, H. N. (1994) Theory of Magnetic Recording-   Bozorth, R. M. (1951) Ferromagnetism-   Crommie, M. F.; Lutz, C. P.; Eigler, D. M. Confinement of electrons    to quantum corrals on a metal surface. (1993) Science, vol. 262, p.    218-20.-   Drexler, K. E. (1991) Nanotechnology 2, 113-118.-   Hristoforou, E.; Chiriac, H.; Neagu, M. A low core mass Linear    Variable Differential Transformers sensor using amorphous wires.    Romanian Journal of Physics, vol. 41, (no. 9-10), Editura Academiei    Romane, 1996. p. 765-9. 4-   Kano, Y.; Hasebe, S.; Huang, C. (Edited by: Suematsu, Y.) New type    LVDT position detector. CPEM '88 Digest. 1988 Conference on    Precision Electromagnetic Measurements, (CPEM '88 Digest. 1988    Conference on Precision Electromagnetic Measurements, Tsukuba,    Japan, 7-10 Jun. 1988.) Tokyo, Japan: Soc. Instrum. & Control    Eng, 1988. p. 95-6. xxi+430-   Midgley, G. W.; Howe, D.; Mellor, P. H. (Edited by: Nicolet, A.;    Belmans, R.) Improved linearity linear variable differential    transformers (LVDTS) through the use of alternative magnetic    materials. Electric and Magnetic Fields. From Numerical Models to    Industrial Applications. Proceedings of the Second International    Workshop, Leuvan, Belgium, 17-20 May 1994.) New York, N.Y., USA:    Plenum, 1995. p. 311-14. xii+376 PP.-   Meydan, T.; Healey, G. W. Linear variable differential transformer    (LVDT): linear displacement transducer utilizing ferromagnetic    amorphous metallic glass ribbons. Sensors and Actuators A    (Physical), vol.A32, (no. 1-3), (EUROSENSORS V Conference, Rome,    Italy, Sep. 30-Oct. 2, 1991.) April 1992. p. 582-7. 5 references.-   Piner, R. D.; Jin Zhu; Feng Xu; Seunghun Hong; Mirkin, C. A. (1999)    “Dip-pen” nanolithography. Science, vol. 283, p. 661-3.-   Young Tae Park; Han Jun Kim; Kwang Min Yu; Rae Duk Lee Study on a    linear variable differential transformer for precision measurements.    Korean Applied Physics, vol. 2, (no. 4), November 1989. p. 347-51. 9    references.-   Saxena, S. C.; Seksena, S. B. L. A self-compensated smart LVDT    transducer. IEEE Transactions on Instrumentation and Measurement,    vol. 38, (no. 3), June 1989. p. 748-53. 6 references.

BACKGROUND OF THE INVENTION

The present invention relates generally to devices that convert verysmall mechanical displacements, as small as the sub-nanometer level,into differential voltages, and vice versa.

One position sensor that has been available since early in the lastcentury to convert mechanical displacements into differential voltages,and vice versa, is the linear variable differential transformer (LVDT).In the conventional commercially available LVDT (Part Number50-00-005XA, Sentech Inc, North Hills, Pa.) depicted in FIG. 1, amoving, ferromagnetic core 1 differentially couples magnetic flux from aprimary coil 2 to two secondary coils 3 and 4. A current is driventhrough the primary coil by an oscillator 5. As the position of the corechanges with respect to the secondary coils, the flux coupled to the twosecondaries changes. These voltages are amplified with a differentialamplifier 6 and converted to a voltage proportional to the coredisplacement by the signal conditioning electronics 7. For smalldisplacements, the signal is linear. The moving core is mechanicallyconnected to the object of interest by a shaft 8. The coils are housedin a shell that also often acts as a magnetic shield 9. Because the core1 is a magnetically soft ferromagnet, it is often desirable to shield itfrom external magnetic fields. The best commercially available LVDTs arelimited to a spatial resolution of 2.5 nm operating in a ±500 nm rangeat a bandwidth of 100 Hz (Lion Precision Model AB-01, Lion Precision,St. Paul, Minn.).

Another position sensor that can convert mechanical displacements intodifferential voltages is one employing capacitive technology.Commercially available capacitive sensors operating in circumstancesanalogous to commercially available LVDTs have surpassed LVDTperformance by nearly an order of magnitude despite relying on signalconditioning circuitry of the same type as that employed for LVDTs (see,for example, the Physik Instrumente Catalog, 2001 edition).Consequently, even though they are difficult to work with andsubstantially more costly (because of more demanding manufacturingrequirements), capacitive sensors are often the components of choice inapplications that require the highest measurement resolution andbandwidth.

Because of their simplicity and low cost, it is of great interest todetermine the sources of the limits in LVDT resolution and how thoselimitations might be overcome. As set forth more fully below, we haveconcluded that the limit on resolution in conventional LVDT resolutionis Barkhausen noise in the ferromagnetic core. Barkhausen noise the namegiven to sudden jumps in the magnetic state of a ferromagnetic material(Bozorth). In ferromagnetic material, defects can lead to special siteswhere domain walls are preferentially pinned. The domain wall can thenbe depinned by thermal energy or an external magnetic field. When thishappens, the domain wall will jump to another metastable pinning site,causing a sudden change in the overall magnetic state of the material.In general, when LVDT cores are formed from ferromagnetic material theflux changes due to Barkhausen noise will not cancel out in adifferential measurement of the two secondaries. This uncanceled noiseleads directly to noise in the core position signal. Furthermore, suddenchanges in the magnetic state of the core can cause changes in thesensitivity of the sensor, again leading to positional noise.

There are a number of schemes to reduce Barkhausen (and electrical)noise in conventional LVDTs, including increasing the primary coil drivecurrent and using amorphous magnetic materials in the core (Meydan, T.,et al.; Hristoforou, E., et al.; and Midgley, G. W., et al.). Whileincreasing the drive current will increase the signal to noise inconventional electronics, it is ineffective when dealing with Barkhausennoise because it creates a larger oscillating magnetic field that can inturn dislodge pinned domain walls more easily leading to increasedpositional noise. Using amorphous magnetic materials has been shown toreduce Barkhausen noise to a small degree but is ultimately ineffectivebecause Barkhausen noise is a fundamental property of ferromagneticmaterials.

Although without an understanding of Barkhausen noise issues, somenon-conventional LVDT designs have eliminated its effects bysubstituting an air core for the ferromagnetic core of the conventionalLVDT. These include a sensor designed for use in a very high magneticfield described by Ellis and Walstrom (U.S. Pat. No. 4,030,085), apin-ball machine described by Kimura (U.S. Pat. No. 4,634,126) and avariety of mechanical gauging applications described by Neff (U.S. Pat.Nos. 2,364,237 and 2,452,862) and Snow (U.S. Pat. No. 2,503,851). Thegauge described by Snow used an excitation scheme where two primarycoils rather than one were excited. One coil was driven at 180 degreesfrom the other, resulting in oscillating magnetic fields from the twoprimaries that tend to cancel each other out. A single air core in thecenter was used as a detector. This is a different excitation schemefrom the one usually used by us and others. Essentially, the roles ofthe primaries and secondaries are reversed. One might expect that fromthe reciprocity theorem (see, for example, Bertram, H. N., Theory ofMagnetic Recording, Cambridge Press, 1994) that the electromagnetics ofthe two situations are identical. However, there are also some necessarydifferences in the noise performance associated with the signalconditioning. In general, the response of the sensors based on air coreLVDTs in the prior art was significantly less sensitive than theimproved sensor described here and would not be suitable for thesub-nanometer, high speed positioning performance we have obtained.Furthermore, the sensors described in the above prior art did not makeuse of any of the improvements we have incorporated into our excitationand signal conditioning electronics. The best performance claimed inthese air-core LVDTs is comparable to current commercially availableLVDTS.

Finally conventional LVDTs are also severely limited in the presence ofan external magnetic field. As the external magnetic field increases,the core saturates and the LVDT becomes ineffectual. This limitation hasbeen addressed by a non-conventional design in which the LVDT isfabricated entirely from non-ferromagnetic material and operated nearthe resonance of the primary and secondary coils (U.S. Pat. No.4,030,085). This design however shares other limitations of conventionalLVDTs in its large length scale and, for this and other reasons, is evenless sensitive than the conventional design.

Present and future nanotechnology depends on the ability to rapidly andaccurately position small objects and tools. Current length scales inmany manufacturing technologies are in the 100 nm range and shrinking.The recording head in a commercial hard disk drive, for example, has awrite gap routinely less than 100 nm and has pole-tip recessioncontrolled to tens of nanometers. The current generation ofsemiconductor integrated circuits uses 180 nm wide traces, with the moveto 130 nm expected within two years and to 100 nm within five years(International Technology Roadmap for Semiconductors, 1999 edition).Current sensors employed to control and verify the lithographicprocesses used in disk drive and IC manufacturing is already only barelyproviding sufficient resolution for critical dimension measurements.

Recent experimental work has gone beyond these relatively largesub-micron scales. Examples include the controlled manipulation ofclusters of molecules (Piner et al.) and even individual atoms (see forexample, Crommie et al.). One goal of nanotechnology is to buildmolecular machines (Drexler, K. E.). If such devices are constructed,they will require precise positioning of individual atoms and molecules.This will require three-dimensional positional information with sub-Aprecision and rapid response as even modest molecular machines inbiological organisms can contain thousands of atoms.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a simple, low cost andhigh resolution sensor that does not require the precision machining ofother high-resolution position sensors or the careful selection,machining or treatment of the magnetic material used in conventionalLVDT cores.

A second object is to provide a high-gain LVDT that does not suffer fromBarkhausen noise.

Another objective is to provide a high-resolution sensor that isinsensitive to temperature variations and does not itself causetemperature variations via eddy current heating of a high-permeabilitycore.

Another objective is to provide a very high-resolution sensor that issuitable for integration with instruments requiring or benefiting fromsuch resolution, including profilometers and scanning probe microscopes,such as atomic force microscopes and molecular force probes.

These and other objects are achieved according to the present inventionby (i) replacing the high permeability core with a low permeability corethat reduces or eliminates Barkhausen noise, (ii) reducing the lengthscale of the LVDT sensor to boost the spatial sensitivity and (iii)improvement in the signal conditioning circuitry.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: Prior Art showing conventional LVDT.

FIG. 2: Preferred embodiment of a low-permeability core LVDT with amoving primary.

FIG. 3: The excitation and synchronous signal conditioning electronicsbased around an analog multiplier.

FIG. 4: The excitation and synchronous signal conditioning electronicsbased around a synchronous analog switch.

FIG. 5: The outputs of the two secondaries as a function of core(conventional LVDT) and primary (preferred embodiment) position.

FIG. 6: Origins of differential Barkhausen noise in conventional LVDTs.

FIG. 7: Origins of common Barkhausen noise in conventional LVDTs.

FIG. 8: The apparatus used to quantify sensor noise and sensitivity.

FIG. 9: LVDT sensor output fit to optical interferometer data showingsensitivity and linearity calibration.

FIG. 10: Noise power spectrum of a conventional (ferromagnetic core) andair core (preferred embodiment) LVDT sensor.

FIG. 11: RMS noise measurements of the several conventional and air coreLVDTs as a function of time.

FIG. 12: RMS noise measurements of the several conventional and air coreLVDTs as a function of primary excitation amplitude.

FIG. 13: Molecular force probe using a piezo actuator and LVDT sensorfor quantitative single molecule force measurements.

FIG. 14: Force curves made over a hard surface with the molecular forceprobe made by plotting the cantilever deflection vs. piezo excitationvoltage and vs. the LVDT sensor.

FIG. 15: Prior art showing a surface imaging profilometer with an LVDTsensor and a magnetic actuator for controlling the loading force.

FIG. 16: A surface imaging profilometer with an air core LVDT sensorthat can also act as a force actuator for controlling probe location andloading force.

FIG. 17: Same as above where the probe is flexured rather than pivoted.

FIG. 18: Prior art showing atomic force microscope.

FIG. 19: Molecular force probe-3D, an AFM based around the MFP head andLVDT sensored x-y precision positioning stage.

FIG. 20: A more detailed diagram of one embodiment of an x-y positionerthat makes use of LVDT position sensors.

FIG. 21: Two AFM images on a diffraction grating. The first (A) shows anuncorrected AFM scan. The second (B) shows an image where the LVDTsensors were used to linearize the stage movement.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 2 shows our improved LVDT position sensor. This LVDT comprises anon-ferromagnetic coil form 14 around which a moving primary coil 15 iswound and two stationary secondary coils 3 and 4 wound around anon-ferromagnetic coil form 10. The primary coil form 14 is mechanicallyconnected to the object of interest (not shown) by a shaft 8. The shaft8 can transmit displacements of the object of interest on the order ofmany microns or smaller. The coil forms can be made of anynon-ferromagnetic material, including but not limited to, plastics,ceramics and composites without ferro-magnetic content, or paramagneticmaterial. Alternatively, the coil forms could be constructed fromnon-ferromagnetic adhesive and the winding or windings. Excitationelectronics 11, more fully described below, produce the current drivingthe primary coil. As the position of the primary coil 15 changes withrespect to the secondary coils 3 and 4, and therefore the object ofinterest attached to shaft 8, the flux coupled to the two secondarieschanges. These voltages are amplified with a differential amplifier 6and converted to a voltage proportional to the core displacement by thesignal conditioning electronics 12, more fully described below. Thearrangement of this LVDT removes ferromagnetic material from the activeportion of the sensor. As discussed below, this improvement lowers thesensitivity gain provided by high permeability magnetic material buteliminates Barkhausen noise. The elimination of Barkhausen noise permitsraising the level of excitation voltage 11 without causing acorresponding increase in output noise, thus increasing the sensitivityof the LVDT. It may be noted that the removal of ferromagnetic materialfrom the active portion of the sensor confers a secondary advantage.There are no longer any constraints on the material chosen for the shellsurrounding the LVDT (not shown). Since there is no ferromagneticmaterial in the core, the sensitivity and noise of the preferredembodiment LVDT is insensitive to external magnetic fields, includingthose generated from the shell material.

FIG. 3 and FIG. 4 show the excitation and signal conditioningelectronics of our improved LVDT position sensor. Both circuits arebased on a square wave oscillator 23, that provides an output at aprecisely defined amplitude and frequency. The excitation electronicsdrive the LVDT primary 15 with a pure sine wave. For this purpose, a lowpass filter 24 that effectively removes all the harmonics of the squarewave above the fundamental is employed. The filter is optimized to bestable with respect to variations in temperature. The resulting highpurity, low distortion sine wave is then amplified by a current buffer25 that drives the LVDT primary 15. The end result of this portion ofthe circuit was a sine wave oscillator with exceptional frequency andamplitude stability.

FIG. 3 shows one version of the signal conditioning electronics of ourimproved LVDT position sensor. One end of each of the secondaries 3 and4 is grounded and the connected to a high precision, low noisedifferential amplifier 6. This differential amplifier is designed toproduce low noise when coupled to a low impedance input source (such asa coil). The output of the differential amplifier 6 is input to a lownoise analog multiplier circuit 27. The output of the filter 24 goesthrough a low noise, precision phase shift circuit 28 and fed as theother input of the multiplier circuit 27. Finally, the output of themultiplier circuit 27 is filtered by another high precision, low noise,stable, low pass filter 29 to remove the frequency doubled component ofthe multiplier output. The output of this filter provides thesynchronous signal proportional to the position of the moving primarycoil 15. Alternatively to phase shifting the reference signal into themultiplier 27, it is possible to phase shift the signal going into theprimary drive current buffer 25. All that matters is that the relativephase of the primary drive and the multiplier reference is adjustable.

FIG. 4 shows another version of the signal conditioning electronics ofour improved LVDT position sensor. The electronics are similar to thoseof FIG. 3 up to the output of the differential amplifier 6. In FIG. 4circuit, the output of the differential amplifier 26 goes into a bufferamplifier 31 and an inverting buffer amplifier 32. The output of thebuffer amplifier 31 is fed into a normally closed input of an analogswitch 33 while the output of the inverting buffer amplifier 32 is fedinto a normally open input of the switch. This arrangement could bereversed with no loss of functionality. The action of the analog switch33 is controlled by a square wave that originates in the square waveoscillator 23 which is phase shifted by a low noise, precision phaseshift circuit 30 before being input to the analog switch 33 so that thetwo parts of the switch are set so that one part is open when the otherpart is closed. Preferably, the opening and closing of the two parts ofswitch 33 occurs 90 degrees out of phase with the output signal fromamplifier 26. The output of the analog switch 33 is fed into a stable,low noise, low pass filter 34. As with the other version, the output ofthis filter provides the synchronous signal proportional to the positionof the moving primary coil 15.

The basic idea behind any LVDT is that the mutual inductances between amoving primary and two secondaries change as a function of position. Theupper panel of FIG. 5 shows the induced voltage at the output of eachsecondary of a conventional LVDT and the described LVDT as a function ofcore position. In both cases, the secondaries were positioned so thatthe outputs cancel at the steepest part of the slope of the inducedvoltage. This insures that the sensitivity of the subtracted voltages tochanges in core or moving primary position is as large as possible. Thedashed lines show the response of the two secondaries in theconventional LVDT. The solid lines show the response of the twosecondaries in our improved LVDT. The sensitivity of the LVDT can becalculated by simply subtracting the outputs of the two secondaries.This is shown for both cases in the lower panel of FIG. 5. Thesensitivity for small excursions of the core around the center point canbe measured by fitting a line around the center. In the case of theconventional LVDT, the raw sensitivity (i.e., slope of the subtractedcurve near the zero point) was 3.16 Volts/mm and in the case of theimproved LVDT it was 0.26 Volts/mm. This points to a notable advantageof using a ferromagnetic core. The permeability of the core materiallyenhances gain, increasing the sensitivity of the LVDT signal.

It is instructive to identify the limits on LVDT resolution. At leastone manufacturer claims that its conventional LVDTs have “infiniteresolution” and that any deviation from perfection is due toshortcomings in the signal conditioning or display (Lion Precision ModelAB-01, Lion Precision, St. Paul, Minn.). This claim is puffery for atleast two reasons. First, coils wound with wire will be subject toJohnson noise (Herceg, Edward E., An LVDT Primer, Sensors, p. 27-30 June(1996). noise. As a result, Johnson noise is present in bothconventional LVDTs and in the LVDT described here. Johnson noise willtranslate into an electric signal at the output of the signalconditioning electronics that will be indistinguishable from actualmotion of the sensor. Second, and probably most important forconventional LVDTs, the use of ferromagnetic materials introduces thephenomenon known as Barkhausen noise. If the ferromagnetic core wereperfect, meaning that the permeability is constant and the magnetizationchanges in a perfectly linear and smooth manner, this phenomenon couldbe ignored. However, ferromagnetic materials are never perfect.Barkhausen noise is the name given to sudden jumps in the magnetic stateof ferromagnetic material. Defects in ferromagnetic material can lead tospecial sites where domain walls are preferentially pinned. The domainwall can then be de-pinned by thermal energy or an external magneticfield. When this happens, the domain wall will jump to anothermetastable pinning site, causing a sudden change in the overall magneticstate of the material.

We have concluded that the current limit on resolution in LVDT sensorsis not signal conditioning or display errors but rather Barkhausen noisein the ferromagnetic core. Because the Barkhausen noise often originatesfrom switching of small volumes of magnetic material, the flux changesin each of the two secondaries will not cancel out in the differentialmeasurement. This in turn leads to noise in the core position signal.FIG. 6 and FIG. 7 show how a Barkhausen jump in the ferromagnetic coreof a conventional LVDT causes positional noise. Both FIG. 6 and FIG. 7show the same components as FIG. 1, the conventional LVDT, except thatthe core 1 of FIG. 1 has been redrawn as a polycrystalline material witha number of defects and grain boundaries that are capable of pinningdomain walls, one of which is identified as 10 a in FIG. 6 and anotheras 10 b in FIG. 7. In FIG. 6, a Barkhausen jump in the small volume ofmaterial 10 a couples more flux into the left hand secondary coil 4 thaninto the right 3. The resulting voltage spike induced in the leftsecondary coil, represented by 11 a, will be larger than the spikeinduced in the left secondary coil, represented by 12 a. When these twovoltage spikes go through the differential amplifier 6 and signalconditioning electronics 7 they cause positional noise, represented by13 a. Another aspect of Barkhausen noise making it difficult to removeis illustrated in FIG. 7. In FIG. 7, the Barkhausen jump has occurred ina grain 10 b that is serendipitously located equidistant between the twosecondaries 3 and 4. Because the jump occurred equidistant from the twosecondaries, the induced voltage spikes, represented by 11 b and 12 bare equal. When these spikes go through the differential amplifier 6 andsignal conditioning electronics 7, they cancel and do not lead topositional noise, represented by 13 b.

We tested the hypothesis that Barkhausen noise is the limiting source ofnoise for high sensitivity position measurements in LVDTs. For thispurpose, we measured the positional noise of (i) a commerciallyavailable LVDT using the as-shipped primary coil and ferromagnetic core(FIG. 1), (ii) commercially available LVDTs in which we had changed themagnetic state of the ferromagnetic core by applying a weak (˜10Oersted) external magnetic field to the core and (iii) a commerciallyavailable LVDT in which we had removed the ferromagnetic core andreplaced it with a non-ferromagnetic coil form around which a new movingprimary coil was wound, the result being functionally equivalent to theLVDT described here.

FIG. 8 shows the mechanical apparatus we used for characterizing thenoise of these different LVDTs. It consists of a mechanical frame 16containing a mechanical flexure 17 attached to the moving LVDT core 18,whether any of the several conventional LVDT cores (FIG. 1) or thenon-ferromagnetic coil form wound with a moving primary coil. The LVDTsecondaries 3 and 4 were connected to the mechanical frame 16, whichacted as a reference. A piezo stack 19 pushed on the flexure assembly,moving it with respect to the mechanical reference. In all measurementsmade with FIG. 8 the piezo was driven with a −15 Volt to +150 Volt 0.1Hz triangle wave and the same excitation and signal conditioningelectronics of FIG. 3 were used. The gain of the signal conditioningelectronics was adjusted to give a nominal positional sensitivity of 1.3μm/V for each measurement. This sensitivity meant that aleast-significant bit (LSB) on our 16-bit data acquisition systemcorresponded to a distance of 0.02 nm.

A temperature stabilized, HeNe laser interferometer 20 andNIST-traceable calibration gratings of the sort commonly used in atomicforce microscopy (Calibration standard, NT-MDT, Moscow, Russia) wereused to calibrate the sensitivity and linearity of the different LVDTs.The beam 21 from the laser interferometer was reflected off of themoving core 18 which for this purpose was fitted with a retroreflector22. We calibrated the different LVDTs by fitting the LVDT response tothe interferometer response. FIG. 9 shows the result of this fitting, apiezo hysteresis curve measured with LVDT (iii) identified above, thefunctional equivalent of our improved LVDT, and with the opticalinterferometer. The LVDT data (solid lines) has been scaled and offsetto match the interferometer data (circles) as closely as possible. Asintended, the fitting process has yielded an LVDT sensitivity of 1.30μm/V. Once the sensitivity of the LVDT has been measured, it is possibleto measure the positional noise. For example, one could measure theresponse of an LVDT to a small movement of the piezo stack as a functionof time.

Because they originate from the microscopic distribution of pinningsites in ferromagnetic material, the details of Barkhausen jumps willdiffer from core to core, even when the cores are constructed from thesame material.¹ Furthermore, because the ferromagnetic core is close toa remanent state for a typical first LVDT measurement, the Barkhausennoise will depend on details of the magnetic history of an individualcore. FIG. 10 shows the amplitude spectra of the residuals offerromagnetic-core and non-ferromagnetic-core LVDT responses as afunction of frequency. These spectra were derived by measuring noiseemanating from the LVDTs in question while at rest and analyzing themeasurements with Fourier techniques. As shown in FIG. 10, the amplitudespectrum of the ferromagnetic-core LVDT decreases as a function offrequency, consistent with measurements of Barkhausen noise, while thenon-ferromagnetic-core LVDT shows a much reduced and flatter curve. Thisis consistent with the absence of Barkhausen noise, but with thepresence of Johnson noise originating in the feedback resistors of thesignal conditioning electronics. The integrated rms noise from 0.1 Hz to1 kHz was 0.19 nm for the non-ferromagnetic-core LVDT and 2.1 nm for theferromagnetic-core LVDT.¹ Urbach defect paper on Barkhausen noise

Ferromagnets are frequently in metastable micromagnetic states. Thesemetastable states are typically relatively far from the ground state.There are numerous paths for the ferromagnet to relax towards the groundstate. This results in phenomena of slow relaxation where the magneticstate will gradually change over long time scales, typically from hoursto days, weeks and even months (see, for example, Bozorth). As themagnetization relaxes towards an ever more stable state, thepermeability and stability of the ferromagnet relative to perturbationsby an external magnetic field will also change. In general, the domainwalls will gradually relax toward a more stable configuration leading tofewer Barkhausen jumps. FIG. 11 shows the measured noise for threeconventional ferromagnetic-core LVDTs and three air-core LVDTs as afunction of time. The noise of all three conventional ferromagnetic-coreLVDTs decreases as a function of time, though not in a smooth manner,and there is considerable variability among the noise level of eachcore. Both observations indicate Barkhausen noise. During the sameperiod of time, the noise of the three air-core LVDTs remained much moreconstant at roughly 0.19 nm and there was little variation among thethree different air cores. This indicates the noise originateselsewhere: for example, in the excitation or signal conditioningelectronics.

One method of increasing the signal to noise is to simply increase thedrive current. If the noise is at some constant value, increasing thedrive current should simply increase the signal to noise. FIG. 12 showsthe noise vs. excitation current curves for three conventionalferromagnetic-core LVDTs and three air-core LVDTs. Air-core noise isroughly inversely proportional to the magnitude of the primary current.This response is consistent with the sensitivity being limited by theexcitation and signal conditioning electronics. The noise vs. drivecurrent curves for the ferromagnetic-core LVDTs all have the oppositetrend. As the drive current increases, the noise also increases. Thisindicates Barkhausen noise. When the primary coil drive currentincreases it creates a larger oscillating magnetic field that candislodge pinned domain walls, in turn leading to increased positionalnoise. In addition, the ferromagnetic-core LVDTs in both FIG. 12 andFIG. 11 show much higher variability in their noise performance. Thistoo indicates that the noise is originating from microscopic magneticvariations in each core, that is Barkhausen noise.

It should be noted that the described LVDT can not only convert motionto voltage, but can, in reverse fashion, convert voltage to motion. Thefollowing applications of the described LVDT make use of one or boththese properties.

Precision Force Measurements. FIG. 13 represents a molecular force probeinstrument used for making localized force measurements and employingthe described LVDT in making such measurements. The instrument measuresforces by measuring the deflection of a flexible cantilever with a sharptip 37 as it pushes or pulls on a sample. High sensitivity deflectionmeasurement apparatus and very sharp tips on the end of the flexiblecantilever permit measurements down to the range of single molecules.Indentation force measurements can also be made by pushing thecantilever tip into the surface. In FIG. 13, the cantilever 37 isilluminated with a low coherence light source 35. The light from thissource is focused onto the cantilever 37 with an adjustable focus lens36. Light reflecting off of the cantilever is collected by an adjustablemirror 38 and guided onto position sensor 39. The position sensorprovides a voltage to a controller for the instrument (not shown) thatis proportional to the deflection of the cantilever. The entire opticaldetection system is enclosed in a rigid, stable capsule 40. The capsuleis attached to the frame of the instrument 44 via flexible couplings orflexures 41 and 42. These couplings allow the capsule 40 to translatevertically with respect to the frame of the instrument 44. A piezo stack43 is used to effect the translation and our improved LVDT sensor, withthe moving primary 15 attached to the moving capsule and the stationarysecondaries 3 and 4 attached to the fixed frame of the instrument,provides positional information.

FIG. 14 shows the importance of the LVDT sensor in making forcemeasurements. Both panels show a force curve made using a Si cantilever(Nanosensors MESP) over a mica surface in air. Panel A of FIG. 14 is aplot of the cantilever deflection vs. the voltage applied to the piezo.The light trace 45 shows the approach curve and the dark trace 46 theretraction curve. The adhesion between the tip and sample is evident inthe retraction curve as is the “snap-off” point 47 at approximately 5.5volts. As will be noted the contact portion of the approach andretraction curves do not have the same slope. This can be explained assome sort of viscoelastic behavior of the tip or the sample or both.However, it can also be explained as an artifact of piezo hysteresis,leaving us with an uncertainty in the interpretation. Panel B of FIG. 14shows the same deflection data, this time plotted as a function of theoutput of our improved LVDT. In this Panel, the contact portions of theapproach and retraction curves 47 now have the same slope, ruling outthe existence of any viscoelastic effects in tip-sample interaction.Furthermore use of our improved LVDT sensor rules out any possibility ofpiezo hysteresis artifacts in the force curves. A secondary advantage ofthe use of our sensor is that it permits direct measurement ofdisplacement (e.g. in microns (as shown) or nanometers) on the x-axis.

Surface Profiling. Conventional LVDT sensors have been used in a varietyof surface profiling instruments, including a number of commerciallyavailable instruments (for example the Dektak 8 from Veeco Instruments,Plainview, N.Y.). FIG. 15 shows one such instrument. It is adapted fromFIG. 1 of U.S. Pat. No. 4,669,300. In this instrument, a sharp tip 48attached to a moving stylus 49 is pivoted around a jewel mechanism 50.The tip is in contact with a sample 51 resting on a stage 52 that isscanned relative to the frame of the instrument 53. The motion of thestylus assembly is measured with an LVDT sensor composed of a coilassembly 54 and high permeability ferromagnetic core 55 that moves withthe stylus assembly. The force between the tip 48 and the sample 51 canbe varied by applying a magnetic field to a magnetic slug 56 attached tothe stylus assembly using a magnetic actuating coil 57 attached to theframe of the instrument 53. One major consideration in this design isshielding the primary coil 55 from the magnetic field emanating from themagnetic actuating coil 57 and slug 56. Any stray field from theactuator would change the magnetic state of the high permeabilityferromagnetic core 55, causing changes in the sensitivity and/orapparent position of the tip of the stylus assembly 48.

Use of the LVDT described here permits substantially improvedprofilometry relative to instruments employing a conventional LVDT. Thisincludes surface profiling at higher speeds and lower forces. Moreover,since it is possible to both sense position and apply a force with ourimproved LVDT, the mass of the instrument can be reduced and its speedincreased while allowing for a simplified design. FIG. 16 shows oneexample of the application of the described LVDT where a dc current 58is summed with the oscillating primary current 5 via a summing amplifier59. Insertion of the dc current allows a force to be exerted along theaxis of the LVDT primary coil 15. In this embodiment, the sharp tip 60is attached to a stylus 61 that is moving on a jewel mechanism 50. Thisentire assembly moves relatively to the sample surface 51. In avariation on this embodiment, the LVDT secondaries 3 and 4 could bedriven with a dc current to increase the applied force. As with the useof the primary drive to exert force, this simultaneous force applicationand sensing are possible because the force drive and the LVDT sensordrive are widely separated in frequency. Since the coil forms of thedescribed LVDT are constructed of non-ferromagnetic material,simultaneous force application and sensing has no effect on thesensitivity or noise of the positional measurement.

FIG. 17 shows another embodiment of a profilometer with an LVDT that isused as both a sensor and an actuator. The components of this embodimentare similar to those shown in FIG. 16 with the exception that the stylus61 is attached to the frame of the instrument 63 (not shown in FIG. 16)via a flexible flexured coupling 62. As with the drive and detectionelectronics described in FIG. 16 the secondary could also be driven witha dc force actuation current while the high frequency sensor signal wassimultaneously measured.

Atomic Force Microscopy. FIG. 18 shows an atomic force microscope (AFM)adapted from FIG. 3 of U.S. Pat. No. Re 34,489. The AFM is a device usedto produce images of surface topography (and other samplecharacteristics) based on information obtained from scanning a sharpprobe on the end of a flexible cantilever over the surface of thesample. Deflections of the cantilever correspond to topographicalfeatures of the sample. Typically, the tip-sample position is rasteredby an arrangement of piezo tube scanners, sometimes constrained byflexures. In FIG. 18, the sample 69 is positioned in three dimensionsusing a piezo tube scanner 70. The deflection of the cantilever ismeasured by an optical lever similar to that shown in FIG. 13. Imagesare made by plotting the deflection or other mechanical properties ofthe cantilever as a function of the x-y position of the sample. Theinstrument can be operated in a number of different imaging modesincluding an oscillatory mode where the tip only makes intermittentcontact with the sample surface. A more detailed description of FIG. 18is to be found in the referenced patent.

FIG. 19 shows a molecular force probe as described in FIG. 13 with AFMfunctionality. The sample 69 has been mounted on a precision x-ypositioning stage 71 permitting the sample to be raster-scannedunderneath the MFP. The MFP measures the cantilever deflection as itinteracts with the sample surface and generates an image using a varietyof imaging modes. In this AFM, unlike the AFM described in FIG. 18,motion along the z-axis is provided by a piezo stack 43 in the MFP, thusdecoupling the x-y position from the z-position. This AFM also allowsexternal conventional microscope optics to be aligned with the z-axis ofthe instrument, this feature being represented by an external objective73 aligned with the cantilever tip through an optical port 72 in the x-ypositioning stage 71. In this arrangement, the sample is scannedrelative to both the MFP and to the external optics. FIG. 20 shows acut-away plan view of one embodiment of an x-y positioning stage thatemploys the described LVDT to provide precise positional information.FIG. 20 shows the x stage 77 carried on the y stage 74. Movement of they-stage is accompanied by movement of the y-axis primary 76 and movementof the x-stage by movement of the x-axis primary 78. These movement aresensed by the y-stage and x-stage secondary coil assemblies, 75 and 79,respectively, each mounted to the non-moving frame of the scanner. Anoptical port 72 in the middle of the positioning stage allows opticalaccess to the sample.

FIG. 21 shows the importance of the described LVDT in generating AFMimages. Both panels show images made with the MFP3D equipped with thex-y positioning stage shown in FIG. 20, the stage that uses our improvedLVDT. The images were made using a Si cantilever (Nanosensors MESP) overa diffraction grating commonly used for calibrating AFMs consisting of aregular square array of square 5 um pits, nominally 180 nm deep. Panel Awas made by simply driving the piezo scanners with a series of trianglewaves and using the voltage applied as the measure of sample movement.Panel A shows a distorted image of the diffraction grating pits. Theyappear neither uniform in size nor do they appear to be in a regulararray. Panel B shows the same diffraction grating, this time imaged withclosed loop positioning based on the signal from the described LVDTsensors. In this image, the pits appear uniform in size and with uniformspacing, as expected. Analogously with their use in the molecular forceprobe, the described LVDT sensors have enabled us to accuratelyreproduce an image of the sample surface by measuring, and correctingfor, piezo hysteresis and creep.

Research, development and manufacturing of devices with micron andsmaller length scales has begun and is accelerating. Recently, IBM hasobtained some results where individual atoms are positioned on a surfacewith a local probe (in this case, the probe of a scanning tunnelingmicroscope). Precision placement of atoms, a goal of molecularmanufacturing will require sub-angstrom positioning of local probes inthree dimensions.

The non-ferromagnetic sensors described here lend themselves to thelength scale reductions required by these new techniques and devices.The sensitivity of the LVDT is proportional to the geometric sensitivityof the mutual inductance $\frac{\mathbb{d}M}{\mathbb{d}x}.$The mutual inductance is proportional to the magnetic energy andinversely proportional to the square of current,$M \propto {\frac{{Magnetic}{\quad\quad}{Energy}}{{Current}^{2}}.}$If we keep the number of turns constant by reducing the wire dimensions,it is easy to show that the mutual inductance is independent of the coillength l. On the other hand, the derivative of the mutual inductance isinversely proportional to the coil length,$\frac{\mathbb{d}M}{\mathbb{d}x} \propto {l^{- 1}.}$Thus the sensitivity,${{Sensitivity} \propto \frac{\mathbb{d}M}{\mathbb{d}x} \propto l^{- 1}},$increases as the LVDT coil lengths decrease. This relationship impliesthat the LVDT sensitivity will only get better as the coil lengthdecreases.

As the length scale of sensors and devices decrease, magnetic sensorshave another advantage. Magnetic forces scale as l⁻⁴. This implies thatthe forces resulting from simply operating the sensor will scalefavorably in the case of a MEMs or smaller sized non-ferromagnetic LVDT.

The described embodiments of the invention are only considered to bepreferred and illustrative of the inventive concept; the scope of theinvention is not to be restricted to such embodiments. Various andnumerous other arrangements may be devised by one skilled in the artwithout departing from the spirit and scope of the invention.

1. A method comprising: using a force detecting element to move a movingcoil part linearly, which moving coil part is formed withoutferromagnetic materials; driving said moving coil part with a drivingsignal, and detecting an induced signal on a stationary coil part whichis formed without ferromagnetic materials, to produce an output signalindicative of a moving relationship between said moving coil part andsaid stationary coil part, said stationary coil part sufficiently closeto said moving coil part such that magnetic flux from said moving coilpart induces a current in said other coil part; and using said outputsignal to detect information from said force detecting elementindicative of a resolution in range of microns or less.
 2. A method asin claim 1, wherein said atomic force detecting element is an atomicforce detecting cantilever that detects a surface profile.
 3. A methodas in claim 1, wherein said atomic force detecting element producesimages of surface topography.
 4. A method as in claim 1, furthercomprising forming said moving coil parts and said stationary coil partsby winding coils around materials without ferromagnetic content, saidwinding comprising pressing at least a part of a wire forming a coilagainst a surface of said materials.
 5. A method as in claim 4, whereinsaid coil form is formed of a material from the group consisting ofplastics, ceramics, a paramagnetic material, or a composite materialwithout ferromagnetic content.
 6. A method as in claim 4, wherein saidcoil form is formed of non ferromagnetic adhesive.
 7. A method as inclaim 1, wherein said using comprises synchronously detecting the outputsignal relative to a drive signal.
 8. A method as in claim 7, whereinsaid synchronously detecting comprises synchronizing detection of acharacteristic of the output signal relative to a characteristic of saiddriving signal.
 9. A method as in claim 8, wherein said synchronizingdetection comprises phase shifting said output signal relative to saiddriving signal.
 10. A method as in claim 7, wherein said synchronouslydetector comprises using a signal indicative of the driving signal todrive a switch.